The $\gamma$-support as a micro-support

Abstract

We prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma$-support of $L$ coincides with the reduced micro-support of its sheaf quantization. As an application, we give a characterization of the Vichery subdifferential in terms of $\gamma$-support.

9 pages, final version

References in corpus (2)

• Exact Lagrangian submanifolds in simply-connected cotangent bundles
• Persistence-like distance on Tamarkin's category and symplectic displacement energy